Page 288 - Compact Numerical Methods For Computers
P. 288
Index 275
Loss of information in least-squares Matrix iteration methods for function
computations, 23, 67 minimisation, 187
Lottery, Matrix product count, 250
optimal operation of, 144, 228 Matrix transpose, 22
LU decomposition, 74 Maxima, 143
Maximal and minimal eigensolutions, 243
McKeown, J. J., 207
Machine arithmetic, 6 Mead, R., 168, 170
Machine precision, 6, 46, 70, 105, 219 Mean of two numbers, 8
Magnetic roots, 232 Measure of work in function minimisation, 227
Magnetic zeros, 147 Method of substitution, 93
Malcolm, M. A., 6 Minima of functions, 142
Mantissa, 6 Minimum-length least-squares solution, 22, 25
Market equilibrium, Model,
nonlinear equations, 231 linear, 23
Marquardt, D. W., 211, 212 nonlinear, 207
Marquardt algorithm, 209, 223, 228, 232, 233 of regional hog supply, 204
Mass-spectrograph calibration, 20 Modular programming, 12
Mathematical programming, 3, 13 Moler, C., 250, 253
Mathematical software, 11 Moler matrix, 127, 250, 253
Matrix, 19 Choleski decomposition of, 91
coefficient, 20.23 Moments of inertia, 125
complex, 110 Moore-Penrose inverse, 26, 44
cross-products, 66 Mostow, G. D., 74
dense, 20, 23 Multiplicity of eigenvalues, 120
diagonal, 26, 3 1 Murray. W., 221, 225, 228
elementary, 73
Frank, 100 NAG, 10, 215
generalised inverse of, 24 Nash, J. C., 33, 56, 63, 70, 110, 134, 137, 196, 211,
Hermitian, 110 215, 226, 235
inverse, 24, 95 Nash, S. G., 82, 148, 235
Moler, 100 Negative definite matrix, 238
non-negative definite, 22, 86 Nelder, J. A., 168, 170
non-symmetric, 110 NelderMead search, 168, 197, 223, 228, 230, 233
null, 52 modifications, 172
orthogonal, 26, 31, 50 Neptune (planet), 131
positive definite, 22 Newing, R. A., 138, 141
rank of, 20 Newton-Raphson iteration, 210
real symmetric, 31, 119 Newton’s method, 161, 188, 210
rectangular, 24, 44 for more than one parameter, 187
semidefinite, 22 Non-diagonal character,
singular, 20 measure of, 126
sparse, 20, 21, 23 Nonlinear equations, 142, 143, 144, 186, 231
special, 83 Nonlinear least-squares, 142, 144, 207, 231
symmetric, 23, 28 Nonlinear model of demand equations, 223
symmetric positive definite, 83, 84, 93 Non-negative definite matrix, 22
triangular, 26, 50, 52, 72, 74 Non-singular matrix, 20
unit, 29, 32 Norm, 17, 21, 66, 243
unitary, 27 Euclidean, 22
Matrix decomposition, of vector, 104
triangular, 74 Normal equations, 22, 25, 41, 50, 55, 66, 92, 239
Matrix eigenvalue problem, 28, 135 as consistent set, 88
generalised, 104, 148 Normalisation, 28, 52
Matrix eigenvalues for polynomial roots, 148 of eigenvectors, 108, 119
Matrix form of linear equations, 19 of vector to prevent overflow, 104
Matrix inverse for linear equations, 24 to prevent overflow, 103
